1. Cosmic Coincidence and Interacting Holographic Dark Energy 胡波 @ ncu 2006.10 Suzhou Dark Universe Workshop

2. Outline  Introduction  The framework  Holographic DE  Interacting DE  The coincidence problem  Discussion Note: Based on hep-th/0601093 by Bo Hu and Yi Ling

3. Introduction  The coincidence problem: “why are the densities of matter and dark energy of precisely the same order today?”  To understand it, we must understand first the nature and dynamical properties of the dark energy.  Based on Holographic principal, a clear description of dark energy can be obtained.  The coincidence problem can be mitigated in interacting DE models.

4. Holographic Dark Energy  holographic hypothesis:  key issue: what possible physical scale one can choose as L constrained by the fact of the current acceleration of the universe.  Example:  Hubble horizon (S. D. H. Hsu, PLB 594, 13)  Future event horizon (M. Li, PLB 603, 1 )

5. Interacting Dark Energy  DM and DE are postulated to be coupled: which lead to  Constraints on Q

6. Interacting Holographic DE  From the first Friedmann equation then one obtains  From the equation of Q  L, Q,  and r are not independent quantities but related by the above equations.

7. Interacting Holographic DE  Constraint or  Example: particle horizon

8. The coincidence problem  In the SM with a c.c. and vanishing Q only when t is around t 0 that r ～ O (1).  Non-vanishing Q may change the dynamics of r greatly.  In interacting holographic dark energy models, the coincidence problem and the holographic nature of dark energy can be studied from different points of views, theoretically or phenomenologically.

9. Example: dr/dt = 0  If then from the Friedmann equation and consequently  Now if then or if L is set to be the future event horizon, then

10. Soft coincidence  dr/dt = 0 can only account for particular situations, e.g. late time evolution of the universe, since at early times, it is hard to obtain a r of O (1) size.  In more realistic models, r may vary slowly with time, which is the case of soft coincidence.  Example: and  = constant, one finds that r will run from an unstable but finite maximum r + to a stable minimum r - at late time, and r + r - = 1. (Chimento, astro-ph/0303145)

11. Soft coincidence  However, it might not be necessary to have both an unstable finite maximum r + and a stable minimum r - close to O (1).  r - is more important in the coincidence problem and presumably is determined by the physics effective at the current evolution of the universe.  whether or not an O (1) initial condition can be obtained is more related to the early evolution of the universe and determined by physics beyond the scope of this talk.

12. Soft coincidence  Concentrating on r - leads to more theoretical possibilities.  For example: if and L is chosen to be the future event horizon, then only one positive stable minimum can be found.

13. Soft coincidence  Another example  The interaction becomes important only at late time and will lead to a stable minimum which can mitigate the coincidence problem.  If  = constant, then  If L is chosen to be the future event horizon,

14. Soft coincidence  One more example and L is chosen to be the future event horizon, then

15. Soft coincidence  Other possibilities can also be explored, such as the case r at late time can be approximated by a power law dependence on a, i.e.

16. Discussion  In interacting holographic dark energy framework, the coincidence problem can be relieved and many theoretical possibilities exist.  More works are necessary for a better understanding of the nature of holographic DE and the interacting DE.  More observational data may help! To shed light on the dark …

17. Thank You!